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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Common fixed points of commuting mappings


Authors: William J. Gray and Carol M. Smith
Journal: Proc. Amer. Math. Soc. 53 (1975), 223-226
MSC: Primary 54H25
DOI: https://doi.org/10.1090/S0002-9939-1975-0377843-1
MathSciNet review: 0377843
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Abstract: Let $ X$ be a dendroid and $ S$ an abelian semigroup of continuous monotone self-mappings of $ X$. A point $ x\epsilon X$ is fixed under $ S$ if $ g(x) = x$ for all $ g\epsilon S$. Let $ f:X \to X$ be continuous and commute with each element of $ S$. It is shown that $ f$ and $ S$ have a common fixed point.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0377843-1
Keywords: Dendroid, abelian semigroup, monotone mapping, open mapping, arc order, hereditarily unicoherent continuum
Article copyright: © Copyright 1975 American Mathematical Society

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